The term "throw one's lot with" means to join or align oneself with a particular group or cause. Some antonyms for this phrase might include "disassociate," "disengage," "dissociate," "withdraw," or "defect." These words convey the opposite sentiment of throwing one's lot with a group, indicating a desire to distance oneself from the group or cause in question. Other potential antonyms might include "oppose," "resist," "reject," or "oppose," which imply active opposition to the group or cause in question rather than mere disassociation. Whatever the specific antonym used, it would convey a sense of moving away from, rather than towards, a particular group or cause.